Duvernay-Tardif will not need surgery and the Chiefs are hopeful he will be available to play in their regular-season opener against the Cleveland Browns on Sept. 12, the source said.
NFL Network was first to report news of Duvernay-Tardif's injury.
Duvernay-Tardif had been running as the second-team right guard behind rookie Trey Smith, a sixth-round draft choice, in training camp.
Duvernay-Tardif, a doctor, opted out of last season to help with COVID-19 patients while working as an orderly at a nursing home in his native Montreal.
Over the previous five seasons, Duvernay-Tardif started 57 regular-season games for the Chiefs and six more in the playoffs. He was their starter at right guard in the Chiefs' win over the San Francisco 49ers in Super Bowl LIV.
The Chiefs began training camp without another candidate to start at right guard. Kyle Long sustained a knee injury while working out during the offseason and has yet to practice with the team at training camp.